LONDON—A plan for a brand new airport for London championed by the city's mayor has failed to secure the backing of a commission studying how to add hub capacity in the U.K.

The Airports Commission, set up in November 2012 to recommend how to best add runway capacity in the south east of England, had in December said that expanding Heathrow, Europe's busiest hub, and London Gatwick were its favored solutions. It deferred a decision...